A simple pendulum is made of a small blob of mass m = 3.000 kg attached to the end of an inextensible wire. The angularamplitude of oscillation is o = 5.730°.Use g =9.807 m/s² for the gravitational acceleration.What is the magnitude T of the tension in the wire when theblob is directly below its point of support?T =

Answered: A simple pendulum is made of a small…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 5PQ

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The angular position of a pendulum is represented by the equation = 0.032 0 cos t, where is in radians and = 4.43 rad/s. Determine the period and length of the pendulum.
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
A particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.
The total energy of a simple harmonic oscillator with amplitude 3.00 cm is 0.500 J. a. What is the kinetic energy of the system when the position of the oscillator is 0.750 cm? b. What is the potential energy of the system at this position? c. What is the position for which the potential energy of the system is equal to its kinetic energy? d. For a simple harmonic oscillator, what, if any, are the positions for which the kinetic energy of the system exceeds the maximum potential energy of the system? Explain your answer. FIGURE P16.73
A nylon siring has mass 5.50 g and length L = 86.0 cm. The lower end is tied to the floor, and the upper end is tied to a small set of wheels through a slot in a track on which the wheels move (Fig. P18.76). The wheels have a mass that is negligible compared with that of the siring, and they roll without friction on the track so that the upper end of the string is essentially free. Figure P18.76 At equilibrium, the string is vertical and motionless. When it is carrying a small-amplilude wave, you may assume the string is always under uniform tension 1.30 N. (a) Find the speed of transverse waves on the siring, (b) The string's vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an antinode at the free top end. Find the node-antinode distances for each of the three simplest states, (c) Find the frequency of each of these states.
A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude of 4.00 cm on a frictionless, horizontal surface. Find (a) the total energy of the system and (b) the speed of the object when its position is 1.00 cm. Find (c) the kinetic energy and (d) the potential energy when its position is 3.00 cm.
In an oscillatory motion of a simple pendulum, the ratio of the maximumangular acceleration, e'max, to the maximum angular velocity, e'max, is 2n s (-1). What is the time needed for the pendulum to complete two oscillations? 0.5 sec 4 sec O 0.25 sec O 1 sec O2 sec A simple pendulum fs made of a 50 en-string ahd a bob.of mass m. At t-0 the O O O O O
A force of 30 N stretches a spring 15 cm. a) What is the mass attached to such a spring if it oscillates on a horizontal frictionless surface with a period of π/4 seconds? b) If the mass is released from rest at t=0 from its amplitude of +5 cm, where will it be and what direction is it moving after π/12 seconds? c) What force does the spring exert on the body when it is +3 cm from its equilibrium position.
The pendulum in the figure consists of a uniform disk with radius r = 15.0 cm and mass 880 g attached to a uniform rod with length L = 570 mm and mass 270 g. (a) Calculate the rotational inertia of the pendulum about the pivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculate the period of oscillation. L.
The spring-mounted 0.68-kg collar A oscillates along the horizontal rod, which is rotating at the constant angular rate d = 8.6 rad/s. At a certain instant, r is increasing at the rate of 660 mm/s. If the coefficient of kinetic friction between the collar and the rod is 0.65, calculate the friction force Fexerted by the rod on the collar at this instant. Vertical Answer: F = i
The balance wheel of a watch oscillates with angular amplitude 0.59?0.59π rad and period 0.18 s. Find (a) the maximum angular speed of the wheel, (b) the angular speed of the wheel at displacement 0.59?/20.59π/2 rad, and (c) the magnitude of the angular acceleration at displacement 0.59?/40.59π/4 rad.
Spring during Christmas? A uniform solid sphere of mass M = 53.7[g] and radius Ris hanged by two ideal springs. The first spring has force constant k₁ = 28.6[N/m], while the second spring has a force constant of k2 19.2[N/m]. When point P is pulled downward with a small displacement y and is then released, the sphere oscillates without slipping. What is the period of small oscillations of the sphere? k₂ Select one: O 0.0942[s] 0.300[s] O 0.188[s] O 0.1333 [s] M k₁ P

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